### Video Transcript

A chemist has five samples of sewage water. They measure the pH values of all the samples at 25 degrees Celsius and record them
in the table below. What is the hydroxide concentration OH−, in units of moles per liter, of sample
one? Give your answer to two decimal places in scientific notation.

The pH values of five samples is given in the table. pH is a way to represent the
concentration of hydronium ions in solution. The concentration of hydronium ions in any aqueous solution at 25 degrees Celsius is
closely related to the hydroxide ion concentration. In fact, at 25 degrees Celsius, the concentration of hydronium ions times the
concentration of hydroxide ions will be equal to one times 10 to the negative
14th. Just as hydronium ion concentration can be represented using pH, hydroxide ion
concentration can be represented using pOH. These four quantities — pH, pOH, hydronium ion concentration, and hydroxide ion
concentration — can be related to one another via six different equations so long as
the temperature of the solution is 25 degrees Celsius.

To answer this question, we need to calculate the hydroxide ion concentration of
sample one, which has a pH of 7.6. Looking at the diagram, we can see that there are two different pathways we could use
to convert the pH to the hydroxide ion concentration. For this video, we’ll start by converting the pH to the hydronium ion concentration,
but first we’ll need to clear some space. To perform this conversion, we can use the equation hydronium ion concentration
equals 10 to the negative pH. After substituting the pH and performing the calculation, we get a numerical value of
2.5118 times 10 to the negative eighth. We should then recognize that even though pH is a dimensionless value, we solved for
a concentration which is given the unit moles per liter.

Now, we can calculate the concentration of hydroxide using the equation hydronium ion
concentration times hydroxide ion concentration equals one times 10 to the negative
14th. Each of the concentrations used in this equation should be in moles per liter, and
yet the constant is a dimensionless value. So, for the purposes of solving this equation, we’ll use the concentration of
hydronium ions without a unit, recognizing that when we solve for the hydroxide ion
concentration, the value will be given the unit moles per liter. After substituting the value for the hydronium ion concentration into the equation
and rearranging to solve, we’ll get a value of 3.9811 times 10 to the negative
seventh, which we’ll recognize should be given the unit moles per liter.

Our answer has the correct unit and is in scientific notation, but we need to give
our answer to two decimal places. Rounding appropriately, we have determined that the hydroxide concentration of sample
one is 3.98 times 10 to the negative seventh moles per liter.